Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{n^2 - 7n}{n^2 + 3n - 70}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 7n}{n^2 + 3n - 70} = \dfrac{(n)(n - 7)}{(n + 10)(n - 7)} $ Notice that the term $(n - 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 7)$ gives: $x = \dfrac{n}{n + 10}$ Since we divided by $(n - 7)$, $n \neq 7$. $x = \dfrac{n}{n + 10}; \space n \neq 7$